# from: http://www.psych.ualberta.ca/~phurd/cruft/g.test.r
#
# Log-likelihood tests of independence & goodness of fit
# Does Williams' and Yates' correction
# does Monte Carlo simulation of p-values, via gtestsim.c
#
# G & q calculation from Sokal & Rohlf (1995) Biometry 3rd ed.
# TOI Yates' correction taken from Mike Camann's 2x2 G-test fn.
# GOF Yates' correction as described in Zar (2000)
# more stuff taken from ctest's chisq.test()
#
# ToDo:
# 1) Beautify
# 2) Add warnings for violations
# 3) Make appropriate corrections happen by default
#
# V3.3 Pete Hurd Sept 29 2001. phurd@ualberta.ca

g.test <- function(x, y = NULL, correct="none",
  p = rep(1/length(x), length(x)), simulate.p.value = FALSE, B = 2000)
{
  DNAME <- deparse(substitute(x))
  if (is.data.frame(x)) x <- as.matrix(x)
  if (is.matrix(x)) {
    if (min(dim(x)) == 1) 
      x <- as.vector(x)
  }
  if (!is.matrix(x) && !is.null(y)) {
    if (length(x) != length(y)) 
      stop("x and y must have the same length")
    DNAME <- paste(DNAME, "and", deparse(substitute(y)))
    OK <- complete.cases(x, y)
    x <- as.factor(x[OK])
    y <- as.factor(y[OK])
    if ((nlevels(x) < 2) || (nlevels(y) < 2)) 
      stop("x and y must have at least 2 levels")
    x <- table(x, y)
  }
  if (any(x < 0) || any(is.na(x))) 
    stop("all entries of x must be nonnegative and finite")
  if ((n <- sum(x)) == 0) 
    stop("at least one entry of x must be positive")
  #If x is matrix, do test of independence
  if (is.matrix(x)) {
    #Test of Independence
    nrows<-nrow(x)
    ncols<-ncol(x)
    if (correct=="yates"){ # Do Yates' correction?
      if(dim(x)[1]!=2 || dim(x)[2]!=2) # check for 2x2 matrix
        stop("Yates' correction requires a 2 x 2 matrix")
      if((x[1,1]*x[2,2])-(x[1,2]*x[2,1]) > 0)
        {
          x[1,1] <- x[1,1] - 0.5
          x[2,2] <- x[2,2] - 0.5
          x[1,2] <- x[1,2] + 0.5
          x[2,1] <- x[2,1] + 0.5
        }
      else
        {
          x[1,1] <- x[1,1] + 0.5
          x[2,2] <- x[2,2] + 0.5
          x[1,2] <- x[1,2] - 0.5
          x[2,1] <- x[2,1] - 0.5
        }
    }

    sr <- apply(x,1,sum)
    sc <- apply(x,2,sum)
    E <- outer(sr,sc, "*")/n
    # are we doing a monte-carlo?
    # no monte carlo GOF?
    if (simulate.p.value){
      METHOD <- paste("Log likelihood ratio (G-test) test of independence\n\t with simulated p-value based on", B, "replicates")
      tmp <- .C("gtestsim", as.integer(nrows), as.integer(ncols),
                as.integer(sr), as.integer(sc), as.integer(n), as.integer(B),
                as.double(E), integer(nrows * ncols), double(n+1),
                integer(ncols), results=double(B), PACKAGE= "ctest")
      g <- 0
      for (i in 1:nrows){
        for (j in 1:ncols){
          if (x[i,j] != 0) g <- g + x[i,j] * log(x[i,j]/E[i,j])
        }
      }
      STATISTIC <- G <- 2 * g
      PARAMETER <- NA
      PVAL <- sum(tmp$results >= STATISTIC)/B
    }
    else {
      # no monte-carlo
      # calculate G
      g <- 0
      for (i in 1:nrows){
        for (j in 1:ncols){
          if (x[i,j] != 0) g <- g + x[i,j] * log(x[i,j]/E[i,j])
        }
      }
      q <- 1
      if (correct=="williams"){ # Do Williams' correction
        row.tot <- col.tot <- 0    
        for (i in 1:nrows){ row.tot <- row.tot + 1/(sum(x[i,])) }
        for (j in 1:ncols){ col.tot <- col.tot + 1/(sum(x[,j])) }
        q <- 1+ ((n*row.tot-1)*(n*col.tot-1))/(6*n*(ncols-1)*(nrows-1))
      }
      STATISTIC <- G <- 2 * g / q
      PARAMETER <- (nrow(x)-1)*(ncol(x)-1)
      PVAL <- 1-pchisq(STATISTIC,df=PARAMETER)
      if(correct=="none")
        METHOD <- "Log likelihood ratio (G-test) test of independence without correction"
      if(correct=="williams")
        METHOD <- "Log likelihood ratio (G-test) test of independence with Williams' correction"
      if(correct=="yates")
        METHOD <- "Log likelihood ratio (G-test) test of independence with Yates' correction"
    }
  }
  else {
    # x is not a matrix, so we do Goodness of Fit
    METHOD <- "Log likelihood ratio (G-test) goodness of fit test"
    if (length(x) == 1) 
      stop("x must at least have 2 elements")
    if (length(x) != length(p)) 
      stop("x and p must have the same number of elements")
    E <- n * p
    
    if (correct=="yates"){ # Do Yates' correction
      if(length(x)!=2)
        stop("Yates' correction requires 2 data values")
      if ( (x[1]-E[1]) > 0.25) {
        x[1] <- x[1]-0.5
        x[2] <- x[2]+0.5
      }
      else if ( (E[1]-x[1]) > 0.25){
        x[1] <- x[1]+0.5
        x[2] <- x[2]-0.5
      }
    }
    names(E) <- names(x)
    g <- 0
    for (i in 1:length(x)){
      if (x[i] != 0) g <- g + x[i] * log(x[i]/E[i])
    }
    q <- 1
    if (correct=="williams"){ # Do Williams' correction
      q <- 1+(length(x)+1)/(6*n)
    }
    STATISTIC <- G <- 2*g/q
    PARAMETER <- length(x) - 1
    PVAL <- pchisq(STATISTIC, PARAMETER, lower = FALSE)
  }
  names(STATISTIC) <- "Log likelihood ratio statistic (G)"
  names(PARAMETER) <- "X-squared df"
  names(PVAL) <- "p.value"
  structure(list(statistic=STATISTIC,parameter=PARAMETER,p.value=PVAL,
            method=METHOD,data.name=DNAME, observed=x, expected=E),
            class="htest")
}
